Anisotropy Contrast in Phonon-Enhanced Apertureless Near-Field Microscopy Using a Free-Electron Laser

We demonstrate the imaging of ferroelectric domains in ${\mathrm{BaTiO}}_3$, using an infrared-emitting free-electron laser as a tunable optical source for scattering scanning near-field optical microscopy and spectroscopy. When the laser is tuned into the spectral vicinity of a phonon resonance, ferroelectric domains can be resolved due to the anisotropy of the dielectric properties of the material. Slight detuning of the wavelength gives rise to a contrast reversal clearly evidencing the resonant character of the excitation. The near-field domain contrast shows that the orientation of the dielectric tensor with respect to the sample surface has a clear influence on the near-field signal.

Figure 1

(a) Sketch of our s-SNOM setup: $s$- or $p$-polarized light (with wave vector $k$) is scattered off an SFM tip close to the ${\mathrm{BaTiO}}_3$ sample surface. The distance $h$ between the tip and the sample is modulated at the frequency $\Omega$. The scattering signal is measured on two different domain types of the ferroelectric sample (dielectric tensor $\widehat{\epsilon }$) with the optical axis either parallel ($a$ domain) or perpendicular ($c$ domain) to the surface. For crystallographic reasons, the domain boundary is a plane oriented at 45° with respect to the sample surface. (b) PFM image of the ${\mathrm{BaTiO}}_3$ single-crystal sample showing the typical stripelike domain distribution. Bright areas correspond to $c$ domains, dark areas to $a$ domains. The complementary technique of PFM allows an independent determination of the ferroelectric domain distribution.

Figure 2

Real (${\epsilon }^{\prime }$) and imaginary (${\epsilon }^{\prime \prime }$) parts of the dielectric function of ${\mathrm{BaTiO}}_3$ in the mid-IR taken from the literature [27]. The two functions ${\epsilon }_c$ and ${\epsilon }_a$ describe the optical response along and perpendicular to the $c$ axis, respectively. The insets show the relevant wavelength range in more detail. Dashed lines indicate ${\epsilon }^{\prime }=-3.0$ for both ${\epsilon }_c$ and ${\epsilon }_a$, where we expect resonant enhancement of the near-field signal.

Figure 3

Distance-dependent near-field spectra recorded on a ${\mathrm{BaTiO}}_3$ $c$ domain. Plotted is the near-field scattering (NFS) signal as a function of wavelength $\lambda$ and tip height $h$ (“approach curve”). The tip was approached to the surface until the damping of the cantilever oscillation started to increase dramatically ($h=0\mathrm{nm}$) corresponding to a mean distance between the tip and the sample of about the cantilever oscillation amplitude of 20 nm. This procedure was repeated for several wavelengths, with the scattering signal being demodulated at $2\Omega$ (left column) and $4\Omega$ (right column). The upper panels display experimental raw data normalized to the incident laser power. The lower panels show the corresponding theoretical data as calculated with the adapted dipole model [15, 29] (see 31 for details). Here the wavelength dependence is included via the $\epsilon$ values of ${\mathrm{BaTiO}}_3$ taken from the literature (see Fig. 2). The resonant region lies between $16.5$ and $17.5\mu \mathrm{m}$, shifting to shorter wavelengths for larger tip-sample separations. This behavior characteristically emphasizes the near-field coupling between the tip and the sample as shown earlier for a SiC sample by Taubner, Keilmann, and Hillenbrand [32].

Figure 4

(a) NFS signal measured at $2\Omega$ in a two-dimensional scan (area $13.4\times 13.4\mu {\mathrm{m}}^2$). The sample area is approximately the same as shown in Fig. 1b. For easier comparison, we tile two scans at $\lambda =17.2$ and $16.7\mu \mathrm{m}$ and depict them in the upper and lower part of the image, respectively. At $\lambda =17.2\mu \mathrm{m}$, the $a$ domains appear bright (i.e., the signal is resonantly enhanced), while at $\lambda =16.7\mu \mathrm{m}$ the contrast is reversed and the $a$ domains appear dark. (b) Near-field scattering signal measured at $2\Omega$ at selected wavelengths along the dashed horizontal line in the upper half of (a) (traces shifted vertically for clarity). At wavelengths shorter than $16.4\mu \mathrm{m}$, we measure no scattering signal. At $16.4\mu \mathrm{m}<\lambda <17\mu \mathrm{m}$, the signal is stronger on the $c$ domains, while for $17\mu \mathrm{m}<\lambda <17.7\mu \mathrm{m}$, the $a$ domains appear brighter. At longer wavelengths, we measure an increasing far-field signal due to increased reflection at the sample for more negative dielectric constants. The dashed vertical lines correspond to $c$ domains, i.e., positions which appear bright at $16.7\mu \mathrm{m}$. All data were taken at a tip-sample mean distance $h$ of 45 nm (cf. Figure 3).